Mathematical Engineering Of Deep Learning
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| Author | : Benoit Liquet |
| Publisher | : CRC Press |
| Total Pages | : 415 |
| Release | : 2024-10-03 |
| Genre | : Computers |
| ISBN | : 1040116884 |
Mathematical Engineering of Deep Learning provides a complete and concise overview of deep learning using the language of mathematics. The book provides a self-contained background on machine learning and optimization algorithms and progresses through the key ideas of deep learning. These ideas and architectures include deep neural networks, convolutional models, recurrent models, long/short-term memory, the attention mechanism, transformers, variational auto-encoders, diffusion models, generative adversarial networks, reinforcement learning, and graph neural networks. Concepts are presented using simple mathematical equations together with a concise description of relevant tricks of the trade. The content is the foundation for state-of-the-art artificial intelligence applications, involving images, sound, large language models, and other domains. The focus is on the basic mathematical description of algorithms and methods and does not require computer programming. The presentation is also agnostic to neuroscientific relationships, historical perspectives, and theoretical research. The benefit of such a concise approach is that a mathematically equipped reader can quickly grasp the essence of deep learning. Key Features: A perfect summary of deep learning not tied to any computer language, or computational framework. An ideal handbook of deep learning for readers that feel comfortable with mathematical notation. An up-to-date description of the most influential deep learning ideas that have made an impact on vision, sound, natural language understanding, and scientific domains. The exposition is not tied to the historical development of the field or to neuroscience, allowing the reader to quickly grasp the essentials. Deep learning is easily described through the language of mathematics at a level accessible to many professionals. Readers from fields such as engineering, statistics, physics, pure mathematics, econometrics, operations research, quantitative management, quantitative biology, applied machine learning, or applied deep learning will quickly gain insights into the key mathematical engineering components of the field.
| Author | : Ronald T. Kneusel |
| Publisher | : No Starch Press |
| Total Pages | : 346 |
| Release | : 2021-12-07 |
| Genre | : Computers |
| ISBN | : 1718501900 |
Math for Deep Learning provides the essential math you need to understand deep learning discussions, explore more complex implementations, and better use the deep learning toolkits. With Math for Deep Learning, you'll learn the essential mathematics used by and as a background for deep learning. You’ll work through Python examples to learn key deep learning related topics in probability, statistics, linear algebra, differential calculus, and matrix calculus as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You’ll also use Python to work through the mathematics that underlies those algorithms and even build a fully-functional neural network. In addition you’ll find coverage of gradient descent including variations commonly used by the deep learning community: SGD, Adam, RMSprop, and Adagrad/Adadelta.
| Author | : Krishnendu Chaudhury |
| Publisher | : Simon and Schuster |
| Total Pages | : 550 |
| Release | : 2024-03-26 |
| Genre | : Computers |
| ISBN | : 1617296481 |
Math and Architectures of Deep Learning bridges the gap between theory and practice, laying out the math of deep learning side by side with practical implementations in Python and PyTorch. You'll peer inside the "black box" to understand how your code is working, and learn to comprehend cutting-edge research you can turn into practical applications. Math and Architectures of Deep Learning sets out the foundations of DL usefully and accessibly to working practitioners. Each chapter explores a new fundamental DL concept or architectural pattern, explaining the underpinning mathematics and demonstrating how they work in practice with well-annotated Python code. You'll start with a primer of basic algebra, calculus, and statistics, working your way up to state-of-the-art DL paradigms taken from the latest research. Learning mathematical foundations and neural network architecture can be challenging, but the payoff is big. You'll be free from blind reliance on pre-packaged DL models and able to build, customize, and re-architect for your specific needs. And when things go wrong, you'll be glad you can quickly identify and fix problems.
| Author | : Anthony L. Caterini |
| Publisher | : Springer |
| Total Pages | : 95 |
| Release | : 2018-03-22 |
| Genre | : Computers |
| ISBN | : 3319753045 |
This SpringerBrief describes how to build a rigorous end-to-end mathematical framework for deep neural networks. The authors provide tools to represent and describe neural networks, casting previous results in the field in a more natural light. In particular, the authors derive gradient descent algorithms in a unified way for several neural network structures, including multilayer perceptrons, convolutional neural networks, deep autoencoders and recurrent neural networks. Furthermore, the authors developed framework is both more concise and mathematically intuitive than previous representations of neural networks. This SpringerBrief is one step towards unlocking the black box of Deep Learning. The authors believe that this framework will help catalyze further discoveries regarding the mathematical properties of neural networks.This SpringerBrief is accessible not only to researchers, professionals and students working and studying in the field of deep learning, but also to those outside of the neutral network community.
| Author | : Marc Peter Deisenroth |
| Publisher | : Cambridge University Press |
| Total Pages | : 392 |
| Release | : 2020-04-23 |
| Genre | : Computers |
| ISBN | : 1108569323 |
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
| Author | : Jay Dawani |
| Publisher | : Packt Publishing Ltd |
| Total Pages | : 347 |
| Release | : 2020-06-12 |
| Genre | : Computers |
| ISBN | : 183864184X |
A comprehensive guide to getting well-versed with the mathematical techniques for building modern deep learning architectures Key FeaturesUnderstand linear algebra, calculus, gradient algorithms, and other concepts essential for training deep neural networksLearn the mathematical concepts needed to understand how deep learning models functionUse deep learning for solving problems related to vision, image, text, and sequence applicationsBook Description Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL. What you will learnUnderstand the key mathematical concepts for building neural network modelsDiscover core multivariable calculus conceptsImprove the performance of deep learning models using optimization techniquesCover optimization algorithms, from basic stochastic gradient descent (SGD) to the advanced Adam optimizerUnderstand computational graphs and their importance in DLExplore the backpropagation algorithm to reduce output errorCover DL algorithms such as convolutional neural networks (CNNs), sequence models, and generative adversarial networks (GANs)Who this book is for This book is for data scientists, machine learning developers, aspiring deep learning developers, or anyone who wants to understand the foundation of deep learning by learning the math behind it. Working knowledge of the Python programming language and machine learning basics is required.
| Author | : Ronald T. Kneusel |
| Publisher | : No Starch Press |
| Total Pages | : 346 |
| Release | : 2021-11-23 |
| Genre | : Computers |
| ISBN | : 1718501919 |
Math for Deep Learning provides the essential math you need to understand deep learning discussions, explore more complex implementations, and better use the deep learning toolkits. With Math for Deep Learning, you'll learn the essential mathematics used by and as a background for deep learning. You’ll work through Python examples to learn key deep learning related topics in probability, statistics, linear algebra, differential calculus, and matrix calculus as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You’ll also use Python to work through the mathematics that underlies those algorithms and even build a fully-functional neural network. In addition you’ll find coverage of gradient descent including variations commonly used by the deep learning community: SGD, Adam, RMSprop, and Adagrad/Adadelta.
| Author | : Jong Chul Ye |
| Publisher | : Springer Nature |
| Total Pages | : 338 |
| Release | : 2022-01-05 |
| Genre | : Mathematics |
| ISBN | : 9811660468 |
The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems. Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
| Author | : Tamoghna Ghosh |
| Publisher | : BPB Publications |
| Total Pages | : 572 |
| Release | : 2022-12-30 |
| Genre | : Computers |
| ISBN | : 9355511930 |
Mathematical Codebook to Navigate Through the Fast-changing AI Landscape KEY FEATURES ● Access to industry-recognized AI methodology and deep learning mathematics with simple-to-understand examples. ● Encompasses MDP Modeling, the Bellman Equation, Auto-regressive Models, BERT, and Transformers. ● Detailed, line-by-line diagrams of algorithms, and the mathematical computations they perform. DESCRIPTION To construct a system that may be referred to as having ‘Artificial Intelligence,’ it is important to develop the capacity to design algorithms capable of performing data-based automated decision-making in conditions of uncertainty. Now, to accomplish this goal, one needs to have an in-depth understanding of the more sophisticated components of linear algebra, vector calculus, probability, and statistics. This book walks you through every mathematical algorithm, as well as its architecture, its operation, and its design so that you can understand how any artificial intelligence system operates. This book will teach you the common terminologies used in artificial intelligence such as models, data, parameters of models, and dependent and independent variables. The Bayesian linear regression, the Gaussian mixture model, the stochastic gradient descent, and the backpropagation algorithms are explored with implementation beginning from scratch. The vast majority of the sophisticated mathematics required for complicated AI computations such as autoregressive models, cycle GANs, and CNN optimization are explained and compared. You will acquire knowledge that extends beyond mathematics while reading this book. Specifically, you will become familiar with numerous AI training methods, various NLP tasks, and the process of reducing the dimensionality of data. WHAT YOU WILL LEARN ● Learn to think like a professional data scientist by picking the best-performing AI algorithms. ● Expand your mathematical horizons to include the most cutting-edge AI methods. ● Learn about Transformer Networks, improving CNN performance, dimensionality reduction, and generative models. ● Explore several neural network designs as a starting point for constructing your own NLP and Computer Vision architecture. ● Create specialized loss functions and tailor-made AI algorithms for a given business application. WHO THIS BOOK IS FOR Everyone interested in artificial intelligence and its computational foundations, including machine learning, data science, deep learning, computer vision, and natural language processing (NLP), both researchers and professionals, will find this book to be an excellent companion. This book can be useful as a quick reference for practitioners who already use a variety of mathematical topics but do not completely understand the underlying principles. TABLE OF CONTENTS 1. Overview of AI 2. Linear Algebra 3. Vector Calculus 4. Basic Statistics and Probability Theory 5. Statistics Inference and Applications 6. Neural Networks 7. Clustering 8. Dimensionality Reduction 9. Computer Vision 10. Sequence Learning Models 11. Natural Language Processing 12. Generative Models
| Author | : Steven L. Brunton |
| Publisher | : Cambridge University Press |
| Total Pages | : 615 |
| Release | : 2022-05-05 |
| Genre | : Computers |
| ISBN | : 1009098489 |
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
